Factoring Polynomials 9x^3y+33x^2y^2+30xy^3?

Question

the answer is 3xy(3x+5y)(x+2y) but i dont know how my teacher got it.

 

Answer 1

Given polynomial s 9x^3y+33x^2y^2+30xy^3

= 9x^3y+15x^2y^2+18x^2y^2+30xy^3

= 3x^2y(3x+5y)+6xy^2(3x+5y)

Take common out (3x+5y) from above expression.

= (3x+5y)(3x^2y+6xy^2)

= (3x+5y)3xy(x+2y)

Factorng of given polynomial iis 3xy(3x+5y)(x+2y).